Iterative averaging, fractal structures

In the following section, the detailed analysis of effective Hall properties of a 3D two-component composite will be carried out based on the fractal structure model and the iterative averaging method. 

A number of interesting results have been obtained (due to our fractal model of structure and the iterative averaging method) for the Hall properties of the composite for example, use of a logarithmic derivative allows one to obtain critical exponents for the effective Hall coefficient (Fig. 39) for various values of the magnetic field H. When cti = a2 (Fig. 40) the effective conductivity is a constant if H = 0 and tends to zero if H —> oo near the percolation threshold. On the left of the percolation threshold (p < pc) the rise in the Hall coefficient is more rapid as the magnetic field increases (Fig. 40). On the right of the percolation threshold (p > pc) the Hall coefficient is practically independent of the concentration p. 

Chaotic fractal sets on rectangular lattices have been used to the define the effective conductivity of the composite material. The effective conductivity of the composite material is defined using the fractal random structure model of a composite and the iteration method of averaging. Comparison of the calculation with experimental data is also given. 

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